To start with, what is a fallacy?
A fallacy is a false belief, still holding on to it.
Should we be aware of them?
I believe we should. It makes us fall prey to them less often.
It is one thing to house a snake in your home.
It is another to house a snake in your home and not be aware of it.
The former makes us more watchful, the latter susceptible of being bitten. So is the case with fallacies.